4 Mr. Ivory on the Elastic Force of Steam 



and the differences from the experimental quantities are in- 

 significant. It appears therefore that, taking the values of 

 A and A^ which have been found, the formula (A) repre- 

 sents the elasticities as exactly as can be wished. In order 

 to reduce it to a proper form for use, I substitute the values 

 of A and A", and arrange the terms according to the powers 

 of x; then, 



lo*'. — — 



JLiL. _ -01 1857 — •00046443 . x + -00000993 . :i-. 



Now we have, _ -r -50 _ 162 + t 



^ ~ 20 ~ 20 ' 



wherefore, by substituting. Logarithms of coefficients. 



log. -^ = -0087466^ -3-9418393, 



— -000015178 t^ . . . —5-1812202, (B) 

 + -000000024825 t^ . . -8-3871228. 

 At the freezing point, t = — 180, and the elasticity by the 

 fornuda conies out 0-1 85, which is not sensibly different fi"om 

 0-2 the experimental quantity. The formula (B) may there- 

 foi-e be considered as very nearly exact in the whole range of 

 Dr. Ure's experiments. 



Beyond Dr. Ure's Table there are only two experiments 

 that I am acquainted with which deserve notice. The first is 

 by Mr. Southern, who makes the elasticity equal to 8 atmo- 

 spheres, or 240 inches of mercury, at 343°'6. In this in- 

 stance t = 131-6, and the elasticity computed by the formula 

 is 264 inches, or 24 inches above the experiment. If this 

 appear a very great difference, it is to be obsei-ved that it cor- 

 responds to a variation of 6°-6 of the thermometer; foi', by the 

 formula, the elasticity is exactly 240 at 337°, when t ,= 125. 

 It is to be observed too that Mr. Southern and Dr. Ure differ 

 from one another in the temperatures of the elasticities which 

 both have determined by their experiments, as will thus ap- 

 pear : 



Elasticity- Mr. Southern. Dr. Ure. 



inches. temp. temp. 



60 250°-3 248 



120 293 -4 290 



Formula. 

 240 343 -6 337 



We may therefore conjectiu-e that the formula does not err 

 much at the great pressure of 8 atmospheres. 



The other experiment is by M. Clement, who makes the 

 elasticity equal to 35 atmospheres at 419°. Now here t = 207, 

 and as the computed elasticity amounts oidy lo 23-8 atmo- 

 spheres, 



